Having the advantage of knowing what happens to Brutus and Cassius, who are defeated by Octavius, Marc Antony, and Lucius, the reader must conclude that Brutus has made a crucial mistake when he does not listen to the advice of Cassius,
You know not what you do; donot consent
That Antony speak in his funeral.
Know you how much the people may be moved
By that which he will utter? (23.2.250-253)
As it turns out, allowing Marc Antony to speak is both detrimental to Brutus and the conspirators as well as devastating to the people of Rome, who, roused by the words of Antony against Brutus and the other ironically called "honorable men," riot and effect a civil war. This civil war is far more damaging to the state than the tyranny of which Julius Caesar is suspected.
Added to the condition of the state that deteriorates because Brutus allows Antony to foment the citizens of Rome, Brutus loses his wife Portia, who dies purportedly from a lingering illness during the time he is gone in battle against Antony and the others who prove formidable. Also, Brutus quarrels with his friend Cassius, and, finally, is defeated in the battle at Philippi by Antony, Octavius, and Lucius. So,in retrospect, had Brutus not allowed Antony to turn the Romans against him and the other conspirators, and had he slain Antony as Cassius suggests in Act II, he probably would have been in a better situation to rule.
Yes Brutus was right to let him do so. His biggest mistake was letting him go second after his own speech. This left him time to think about how to dismantle the reputation of the Senate who he called "honorable men". By Brutus letting Antony speak, he was trying to show the crowd that the Senate was not barbaric or murderous. Unfortunately for him, Antony lets the crowd make their own decision (or lets just say Antony leads them). If the people didn't get Brutus, his conscience (the ghost of caesar) would have.